516 



SCIENCE 



[N. S. Vol. XXXVIII. No. 



equation as obtained by the method of the eye 

 and ear is well established. The same fond 

 hopes lay at the basis of introducing the 

 " impersonal " micrometer ; and again there 

 has been a great reduction in x>ersonal equa- 

 tion. The evidence in favor of annihilation, 

 however, is inconclusive. Though many as- 

 tronomers have succeeded in reducing the 

 equation to practically within the limits of 

 accidental error, and some have mads so bold 

 as to affirm that the equation has entirely dis- 

 appeared, there yet remain other astronomers 

 who have not been able to verify these conclu- 

 sions — witness the experiences at Ottawa. As 

 likely as not, history will repeat itself. 



Even if personal equation has not been 

 annihilated, nevertheless, astronomers now 

 possess an advantage that formerly was not 

 theirs ; and that is, that with present facilities 

 it is possible entirely to dissipate the effect of 

 personal equation in longitude determinations. 

 For the variation of personal equation, gen- 

 erally conceded to be the chief source of longi- 

 tude error, may, now that the personal equa- 

 tion itself has become so much lessened, be 

 looked upon as lessened to a corresponding 

 degree, which makes it negligible; and the 

 small residual amount of personal equation 

 left in the observations by the right-ascension 

 micrometer may be made to disappear through 

 exchange of observers. 



It is only in the iinest class of longitude 

 work that the precaution of exchanging ob- 

 servers is deemed necessary. For ordinary 

 geodetic purposes, since personal equation has 

 become so small as to be termed negligible, 

 this precaution is believed to be needless. 

 The introduction of the transit micrometer 

 has consequently led to radical changes in the 

 methods and program of survey longitude op- 

 erations. " The program of longitude observa- 

 tions was formerly designed to eliminate the 

 personal equation " (p. 79) ; and variation of 

 personal equation is a bugbear no longer to 

 be feared. The influence on the time and 

 expense connected with longitude work (p. 94) 

 may be estimated from the fact that it has 

 been found possible, in accordance with Pro- 

 fessor Hayford's prediction of 1904, without 



loss of accuracy, to reduce the original pro- 

 gram of ten nights' observing to three or four. 

 It should be noted, however, that even with 

 the method of the key, " a reduction of the 

 number of nights per station to six, or even 

 four, would result in but slight decrease in 

 accuracy " (p. 94) . 



Before leaving the topic of personal equa- 

 tion it may be well to call attention to another 

 form of this equation, the bisection error. 

 On page 90 the writer believes that for ordi- 

 nary geodetic purposes this is too small to be 

 considered. This may or may not be true; 

 and it may make a difference whether a single 

 or a double thread be employed. Contradic- 

 tory evidence may be found in " A Test of a 

 Transit Micrometer," above cited (p. 472), 

 and " Report of the Chief Astronomer," Ot- 

 tawa, 1909 (pp. 576 et seq.). By reversal during 

 the transit of each star, as already mentioned, 

 the bisection error is automatically eliminated 

 from observations made with the broken-back 

 telescope. With the straight telescope, this 

 elimination may be effected, not from each 

 individual star, but from the clock correction, 

 by a suitable selection of stars north and 

 south of the zenith. 



Returning to the survey observing program, 

 another innovation involves the sets of stars 

 comprising a time determination for longi- 

 tude. The former custom of requiring gen- 

 erally four half -sets is still retained; but the 

 nature of the sets is greatly changed. Where 

 formerly it was customary to observe four 

 clock stars and one azimuth star to each half- 

 set, the clock stars chosen with balanced A 

 factors, the practise now is to eliminate the 

 azimuth star entirely, and to replace it by two 

 additional clock stars. As the interval of time 

 required to observe each star is less than by 

 the method of the key, the total time employed 

 is not greater than before. The argument is, 

 that as the azimuth of the instrument, owing 

 to the balancing of the A factors, has but 

 little effect upon the resulting time determina- 

 tion, it is preferable, rather than to attempt 

 determining this azimuth accurately with an 

 azimuth star, to strengthen the clock correc- 

 tion by observing additional time stars. For 



